210+ Discrete Structure (DS) Solved MCQs

These multiple-choice questions (MCQs) are designed to enhance your knowledge and understanding in the following areas: Computer Science Engineering (CSE) .

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1.	Let A={a, b, {c, d}, e}. How many elements does A contain?
A.	1
B.	2
C.	3
D.	4
Answer» D. 4

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2.	Let A={2,{4,5},4} Which statement is correct?
A.	5 is an element of A.
B.	{5} is an element of A.
C.	{4, 5} is an element of A.
D.	{5} is a subset of A.
Answer» C. {4, 5} is an element of A.

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3.	Which of these sets is finite?
A.	{x \| x is even}
B.	) {1, 2, 3,...}
C.	{1, 2, 3,...,999,1000}
D.	none
Answer» C. {1, 2, 3,...,999,1000}

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4.	Which of these sets is not a null set?
A.	A = {x \| 6x = 24 and 3x = 1}
B.	B = {x \| x + 10 = 10}
C.	C = {x \| x is a man older than 200 years}
D.	D = {x \| x < x}
Answer» B. B = {x \| x + 10 = 10}

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5.	. Let S={1, 2, 3}. How many subsets does S contain?
A.	3
B.	6
C.	8
D.	4
Answer» C. 8

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6.	. Which set S does the power set 2S = {Ф,{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} come from?
A.	{{1},{2},{3}}
B.	{1, 2, 3}
C.	{{1, 2}, {2, 3}, {1, 3}}
D.	{{1, 2, 3}}
Answer» B. {1, 2, 3}

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7.	Let A = {x, y, z}, B = {v, w, x}. Which of the following statements is correct?
A.	A U B ={v, w, x, y, z}
B.	A U B = {v, w, y, z}
C.	A U B = {v, w, x, y}
D.	A U B ={x, w, x, y, z}
Answer» A. A U B ={v, w, x, y, z}

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8.	which sets are equal ? 1.{r,s,t} 2.{s,s,t,r} 3.{t,r,t,s}
A.	1 and 2
B.	2 and 3
C.	1 and 3
D.	all are equal
Answer» D. all are equal

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9.	A U A=A according to …….law
A.	Associative law
B.	commutative law
C.	Indempotent law
D.	distributive law
Answer» C. Indempotent law

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10.	In any application of the theory of sets, the members of all the sets belongs to …… set
A.	union
B.	intersection
C.	universal
D.	cardinal
Answer» C. universal

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11.	let A={{a,b}} then aЄ A
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» B. FALSE

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12.	ФЄФ
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» B. FALSE

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13.	The sets {a,b,c} and {b,c,a} represnet the same sets.
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» A. TRUE

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14.	Cardinality of a set is number of element of the set.
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» A. TRUE

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15.	Multiset is an unordered collection of elemnts where an element can occur a a member more than once
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» A. TRUE

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16.	one of the A or B is uncountably infinite and one is countably infinite then \| AUB\| will be
A.	countably infinite
B.	uncountably finite
C.	countably finite
D.	uncountably infinite
Answer» D. uncountably infinite

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17.	Sum of first n positive integers is
A.	n(n+1)
B.	n
C.	n(n+1)0.5
D.	n(n+2)
Answer» C. n(n+1)0.5

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18.	Let P(S) denote the power set of set S. which of the is always true
A.	P(P(s))=p(s)
B.	P(S)∩ S= P(S)
C.	P(S)∩P(P(S)) ={Ф}
D.	None
Answer» C. P(S)∩P(P(S)) ={Ф}

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19.	{3}Є{1,3,5}
A.	TRUE
B.	FALSE
C.	Both
D.	None
Answer» B. FALSE

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20.	consider the following data for 120 mathematics students at a college concerning the languages French,Gernan, and russian: 65 study frensh, 45 study german 42 study russian , 20 study french and german, 25 study french and russian, 15 study german and russian. 8 study all three languages. Determine how many students study exactly 1 subject?
A.	100
B.	25
C.	56
D.	20
Answer» C. 56

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21.	……… is an unordered collection of elements where an element can occur as a member more than once
A.	Multiset
B.	ordered set
C.	set
D.	None
Answer» A. Multiset

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22.	In a room containing 28 females, there are 18 females who speak English, 15 females speak french and 22 speak german. 9 females speak both english and french, 11 females speak both french and german where as 13 speak both german and english. How many females speak all 3 languages?
A.	9
B.	8
C.	7
D.	6
Answer» D. 6

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23.	If U = {1, 2, 3, . . . 10 } and S = { 4, 5, 6, 7, 8 }, then S ' =
A.	{ 9, 10 }
B.	{1, 2, 3 }
C.	{1, 2, 3 9 }
D.	{1, 2, 3 9 10 }
Answer» D. {1, 2, 3 9 10 }

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24.	If U = {1, 2, 3, . . . 20 } and S = set of prime numbers , then S =
A.	{ 3, 5, 7, 11, 13, 17 }
B.	{ 2, 3, 5, 7, 11, 13, 17, 19 }
C.	{1, 3, 5, 7, 9, 11, 13, 15, 17, 19 }
D.	{1, 2, 3, 5, 7, 11, 13, 17 }
Answer» B. { 2, 3, 5, 7, 11, 13, 17, 19 }

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25.	Consider the statement,“If n is divisible by 30 then n is divisible by 2 and by 3 and by 5.”Which of the following statements is equivalent to this statement?
A.	If n is not divisible by 30 then n is divisible by 2 or divisible by 3 or divisible by 5
B.	If n is not divisible by 30 then n is not divisible by 2 or not divisible by 3 or not divisible by 5
C.	If n is divisible by 2 and divisible by 3 and divisible by 5 then n is divisible by 30.
D.	If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30
Answer» D. If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30

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26.	Which of the following statements is the contrapositive of the statement, “You win the game if you know the rules but are not overconfident.”
A.	If you lose the game then you don’t know the rules or you are overconfident.
B.	A sufficient condition that you win the game is that you know the rules or you are not over confident
C.	If you don’t know the rules or are overconfident you lose the game.
D.	If you know the rules and are overconfiden t then you win the game.
Answer» A. If you lose the game then you don’t know the rules or you are overconfident.

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27.	A sufficient condition that a triangle T be a right triangle is that a2 + b2 = c2. An equivalent statement is
A.	If T is a right triangle then a2 + b2 = c2.
B.	If a2 + b2 = c2 then T is a right triangle.
C.	If a2 + b2 6= c2 then T is not a right triangle.
D.	T is a right triangle only if a2 + b2 = c2.
Answer» B. If a2 + b2 = c2 then T is a right triangle.

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28.	Which of the following is the inverse of the statement: " If I eat a mango than I do not drink milk".
A.	I drink milk only if I do not eat a mango
B.	If I don’t eat a mango then I drink milk
C.	If I do not drink milk then I eat mango
D.	None
Answer» B. If I don’t eat a mango then I drink milk

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29.	If p= It is hot, and q= It is sultry, which of the following sentences in the appropriate version for the symbolic expression: -p٨ q
A.	If it is sultry then it is hot
B.	It is sultry only if it is hot
C.	It is sultry and it is not hot
D.	None
Answer» D. None

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30.	which of the following is the contrapositive of the statement: " A quadrilateral is a square only if it is both rectangle and a rhombus".
A.	If a rectangle is not a a rhombus it is not a square
B.	If a rhombus is not rectangle it is not a square
C.	If a quadrilateral is neither a rectangle nor a rhombus then it is not a square
D.	None
Answer» C. If a quadrilateral is neither a rectangle nor a rhombus then it is not a square

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31.	For a conditional statement p===>q, which of the following is incorrect.
A.	Converse of the inverse is its contrapositive
B.	contrapositive of the converse is its inverse
C.	Inverse of the contrapositiv e is its converse
D.	None
Answer» D. None

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32.	Which of the following is equivalent to p==>q
A.	~xp٨q
B.	pV~q
C.	~xpVq
D.	pV~q
Answer» C. ~xpVq

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33.	Equivalent inverse of p==>q is
A.	~xp٨q
B.	pV~q
C.	~xpVq
D.	pV~q
Answer» D. pV~q

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34.	Converse of p==>q is
A.	~xp٨q
B.	pV~q
C.	~xpVq
D.	pV~q
Answer» D. pV~q

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35.	the truth table for exclusive disjunction will be
A.	tautology
B.	Contradiction
C.	Logical equivalent
D.	p or q but not both
Answer» D. p or q but not both

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36.	The conditional statement p→q and its contrapositive are….
A.	Converse
B.	Inverse
C.	Logically equivalent
D.	None
Answer» C. Logically equivalent

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37.	Set A has 3 elements, set B has 6 elements, then the minimum number of elements in A U B is ….
A.	3
B.	6
C.	9
D.	None
Answer» B. 6

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38.	Set A has 3 elements, set B has 6 elements, then the minimum number of elements in A U B is ….
A.	6
B.	9
C.	18
D.	None
Answer» B. 9

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39.	if P∩ Q= Ф then P U Q' is
A.	P
B.	U-P
C.	U-Q
D.	Ф
Answer» C. U-Q

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40.	The number of proper subset of {1,2,3,4} is
A.	16
B.	15
C.	10
D.	12
Answer» A. 16

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41.	Consider the four statements: 1.(q==>p)٨(~p) 2. p==>(~q) V r 3. ~p==>~(p٨q) 4.p٨q٨~(pVq) Which one is tautology.
A.	A
B.	B
C.	C
D.	D
Answer» C. C

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42.	Which among the statements given in Q.70 is contradiction
A.	A
B.	B
C.	C
D.	D
Answer» D. D

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43.	Consider the four statements 1.p٨~q↔~p V q 2.p٨(~p Vq)٨(~q) 3.(pV(~q))٨ ~((~p)Vq) 4.~(p↔q)↔(p↔~q) which one of this contradiction.
A.	A
B.	B
C.	C
D.	D
Answer» D. D

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44.	consider the four tsatements: 1.(p→q) ٨(p٨~q) 2.(~p→r)٨(p↔q) 3.p→(~qVr) 4.~(p٨q) V (p↔q) Which one of these four ststements is a tautology.
A.	A
B.	B
C.	C
D.	D
Answer» D. D

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45.	In above question which statement is contradiction.
A.	A
B.	B
C.	C
D.	D
Answer» A. A

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46.	Which of the following sets are equal. 1. {p,q,m,n} 2.{m,p,n,q} 3.{q,p,p,m,m,p,n} 4.{p,q,n,,n,m}
A.	1 and 2 are equal
B.	2 and 3 are equal
C.	3 and 4 are equal
D.	All are equal.
Answer» D. All are equal.

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47.	Consider the set A={{1,3,5},{7,9,11},{13,15}} then determine which of the following is/are true. 1.1ЄA 2.{{1,3,5}} CA 3. Ф subet of A 4. A
A.	2 and 3 is true
B.	1 and 3 is true
C.	3 is true
D.	None
Answer» A. 2 and 3 is true

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48.	Determine the validity of the following argument: S1: all my friends are musicians. S2: John is my friend. S3: None of my neighbours are musicians. S: John is not my neighbour.
A.	Valid
B.	Not valid
C.	Both a and b
D.	None
Answer» A. Valid

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49.	In a survey of 60 people , it was found that: 25 read Newsweek magzine. 26 read Time 26 read Fortune 9 read both newsweek and fortune 11 read both Newsweek and Time 8 read both Time and Fortune 3 read all 3 magzines. 1. Find the number of people who read at least one of the three magzines
A.	30
B.	52
C.	40
D.	68
Answer» B. 52

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50.	In above Q.78 Find the number of people who read exactly 1 magzine.
A.	30
B.	52
C.	40
D.	68
Answer» A. 30

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210+ Discrete Structure (DS) Solved MCQs

Let A={a, b, {c, d}, e}. How many elements does A contain?

Let A={2,{4,5},4} Which statement is correct?

Which of these sets is finite?

Which of these sets is not a null set?

. Let S={1, 2, 3}. How many subsets does S contain?

. Which set S does the power set 2S = {Ф,{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} come from?

Let A = {x, y, z}, B = {v, w, x}. Which of the following statements is correct?

which sets are equal ? 1.{r,s,t} 2.{s,s,t,r} 3.{t,r,t,s}

A U A=A according to …….law

In any application of the theory of sets, the members of all the sets belongs to …… set

let A={{a,b}} then aЄ A

ФЄФ

The sets {a,b,c} and {b,c,a} represnet the same sets.

Cardinality of a set is number of element of the set.

Multiset is an unordered collection of elemnts where an element can occur a a member more than once

one of the A or B is uncountably infinite and one is countably infinite then | AUB| will be

Sum of first n positive integers is

Let P(S) denote the power set of set S. which of the is always true

{3}Є{1,3,5}

……… is an unordered collection of elements where an element can occur as a member more than once

In a room containing 28 females, there are 18 females who speak English, 15 females speak french and 22 speak german. 9 females speak both english and french, 11 females speak both french and german where as 13 speak both german and english. How many females speak all 3 languages?

If U = {1, 2, 3, . . . 10 } and S = { 4, 5, 6, 7, 8 }, then S ' =

If U = {1, 2, 3, . . . 20 } and S = set of prime numbers , then S =

Consider the statement,“If n is divisible by 30 then n is divisible by 2 and by 3 and by 5.”Which of the following statements is equivalent to this statement?

Which of the following statements is the contrapositive of the statement, “You win the game if you know the rules but are not overconfident.”

A sufficient condition that a triangle T be a right triangle is that a2 + b2 = c2. An equivalent statement is

Which of the following is the inverse of the statement: " If I eat a mango than I do not drink milk".

If p= It is hot, and q= It is sultry, which of the following sentences in the appropriate version for the symbolic expression: -p٨ q

which of the following is the contrapositive of the statement: " A quadrilateral is a square only if it is both rectangle and a rhombus".

For a conditional statement p===>q, which of the following is incorrect.

Which of the following is equivalent to p==>q

Equivalent inverse of p==>q is

Converse of p==>q is

the truth table for exclusive disjunction will be

The conditional statement p→q and its contrapositive are….

Set A has 3 elements, set B has 6 elements, then the minimum number of elements in A U B is ….

Set A has 3 elements, set B has 6 elements, then the minimum number of elements in A U B is ….

if P∩ Q= Ф then P U Q' is

The number of proper subset of {1,2,3,4} is

Consider the four statements: 1.(q==>p)٨(~p) 2. p==>(~q) V r 3. ~p==>~(p٨q) 4.p٨q٨~(pVq) Which one is tautology.

Which among the statements given in Q.70 is contradiction

Consider the four statements 1.p٨~q↔~p V q 2.p٨(~p Vq)٨(~q) 3.(pV(~q))٨ ~((~p)Vq) 4.~(p↔q)↔(p↔~q) which one of this contradiction.

consider the four tsatements: 1.(p→q) ٨(p٨~q) 2.(~p→r)٨(p↔q) 3.p→(~qVr) 4.~(p٨q) V (p↔q) Which one of these four ststements is a tautology.

In above question which statement is contradiction.

Which of the following sets are equal. 1. {p,q,m,n} 2.{m,p,n,q} 3.{q,p,p,m,m,p,n} 4.{p,q,n,,n,m}

Consider the set A={{1,3,5},{7,9,11},{13,15}} then determine which of the following is/are true. 1.1ЄA 2.{{1,3,5}} CA 3. Ф subet of A 4. A

Determine the validity of the following argument: S1: all my friends are musicians. S2: John is my friend. S3: None of my neighbours are musicians. S: John is not my neighbour.

In a survey of 60 people , it was found that: 25 read Newsweek magzine. 26 read Time 26 read Fortune 9 read both newsweek and fortune 11 read both Newsweek and Time 8 read both Time and Fortune 3 read all 3 magzines. 1. Find the number of people who read at least one of the three magzines

In above Q.78 Find the number of people who read exactly 1 magzine.